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Problem 9.38

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Date Posted: 5/12/2008 12:51:27 AM  Status: Live
Problem 9.38
Course Textbook Chapter Problem
Analog Circuits Electric Circuits (8th) by Nilsson 9 38P
Question Details:
9.38: The circuit shown in fig. P9.38 is operating in the sinusoidal steady state. The capacitor is adjusted until the current Ig is in phase with the sinusoidal voltage Vg.
 
a) Specify the capacitance in microfarads if Vg = 250cos(1000t)V.
 
Now my question comes in. Because the circuit is tuned for resonant frequency, the voltage and current are in phase, can't you just use the ω = √(1/LC) equation to solve for the C value? Or is it not right because it's in parallel with a resistor?
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Date Posted: 5/12/2008 8:10:05 AM  Status: Live
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Response:
(a)
Given voltage function
Now we have to find the current and make the phase of the current equal to voltage.
       
 
Total Impedance
To make the current phase equivalent to voltage phase, the phase of the impedence must be zero.
Given
Therefore
 or
These two values of capacitor can validate the condition
(1)
When then
(2)
Whenthen
 
NOTE:
As you assumed a resistor is parallel with the capacitor, so resonant frequency method is not a valid one.
 
I hope this helps you.....
 
 
Bavatar's Comment:
Thank you a lot, much clearer that the previous answer.



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